scholarly journals Periodic Triangulations of $\mathbb{Z}^n$

10.37236/8298 ◽  
2020 ◽  
Vol 27 (2) ◽  
Author(s):  
Mathieu Dutour Sikirić ◽  
Alexey Garber
Keyword(s):  
A Priori ◽  
Central Symmetry ◽  
Delaunay Tessellations ◽  
Centrally Symmetric ◽  
New Phenomena

We consider in this work triangulations of $\mathbb{Z}^n$ that are periodic along $\mathbb{Z}^n$. They generalize the triangulations obtained from Delaunay tessellations of lattices. In certain cases we impose additional restrictions on such triangulations such as regularity or invariance under central symmetry with respect to the origin; both properties hold for Delaunay tessellations of lattices. Full enumeration of such periodic triangulations is obtained for dimension at most $4$. In dimension $5$ several new phenomena happen: there are centrally-symmetric triangulations that are not Delaunay, there are non-regular triangulations (it could happen in dimension $4$) and a given simplex has a priori infinitely many possible adjacent simplices. We found $950$ periodic triangulations in dimension $5$ but finiteness of the whole family is unknown.

Ball characterizations in spaces of constant curvature

2018 ◽  
Vol 55 (4) ◽  
pp. 421-478
Author(s):  
Jesus Jerónimo-Castro ◽  
Endre Makai, Jr.
Keyword(s):  
Convex Sets ◽  
Central Symmetry ◽  
Connected Components ◽  
Plane Convex ◽  
Converse Implication ◽  
Plane Convex Body ◽  
Dual Theorem ◽  
Centrally Symmetric ◽  
Whole Space ◽  
Straight Lines

High proved the following theorem. If the intersections of any two congruent copies of a plane convex body are centrally symmetric, then this body is a circle. In our paper we extend the theorem of High to spherical, Euclidean and hyperbolic spaces, under some regularity assumptions. Suppose that in any of these spaces there is a pair of closed convex sets of class C+2 with interior points, different from the whole space, and the intersections of any congruent copies of these sets are centrally symmetric (provided they have non-empty interiors). Then our sets are congruent balls. Under the same hypotheses, but if we require only central symmetry of small intersections, then our sets are either congruent balls, or paraballs, or have as connected components of their boundaries congruent hyperspheres (and the converse implication also holds). Under the same hypotheses, if we require central symmetry of all compact intersections, then either our sets are congruent balls or paraballs, or have as connected components of their boundaries congruent hyperspheres, and either d ≥ 3, or d = 2 and one of the sets is bounded by one hypercycle, or both sets are congruent parallel domains of straight lines, or there are no more compact intersections than those bounded by two finite hypercycle arcs (and the converse implication also holds). We also prove a dual theorem. If in any of these spaces there is a pair of smooth closed convex sets, such that both of them have supporting spheres at any of their boundary points Sd for Sd of radius less than π/2- and the closed convex hulls of any congruent copies of these sets are centrally symmetric, then our sets are congruent balls.

Conditions equivalent to central symmetry of convex curves

1964 ◽  
Vol 60 (4) ◽  
pp. 779-785 ◽  
Author(s):  
P. C. Hammer ◽  
T. Jefferson Smith
Keyword(s):  
Central Symmetry ◽  
Maximal Length ◽  
Convex Curves ◽  
The Family ◽  
Centrally Symmetric ◽  
Planar Body

In this paper we establish that a convex planar body C is centrally symmetric provided either one of the following conditions hold:(1) Each line halving the circumference of the boundary γ of C is a diametral line.(A diametral line is a line intersecting C in a chord of maximal length in the family of parallel chords.)(2) Each line halving the area of C is a diametral line.

scholarly journals Central Symmetry of Star-Shaped Flat Bodies

2020 ◽  
pp. 119-123
Author(s):  
I.V. Polikanova
Keyword(s):  
Basic Result ◽  
Convex Bodies ◽  
Slight Modification ◽  
Additive Functional ◽  
The Body ◽  
Central Symmetry ◽  
Geometric Moments ◽  
Centrally Symmetric ◽  
Be Star ◽  
Pass Through

Well-known criteria for the central symmetry are formulated for convex bodies. This study relates to a broader class of star-shaped bodies but is limited by the dimension of 2. The paper introduces the concepts of a sector and a segment of a flat star-shaped body.The basic result is the following. Let a flat body K be star-shaped with respect to its interior point o. On the set of sectors and segments of K, a simply additive, monotonic, and invariant with respect to central symmetry with the center o functional F is given. The body K is centrally symmetric with respect to the center o if and only if every chord passing through the point o divides K into two sectors with equal values of the functional F.The method of proof is — "on the contrary".When considering quantities having geometric meaning (central geometric moments, area) as such functionals, we get both new and known (for an area) statements for flat convex bodies. A slight modification of the proof allows us to obtain a similar statement for the perimeter (an additive functional, but simply not an additive functional on the set of convex flat bodies): flat convex body has its central symmetry if and only if all the chords, dividing the perimeter into halves, pass through one point.

Application of cross correlation to HREM images of surfaces

1987 ◽  
Vol 45 ◽  
pp. 754-755
Author(s):  
D. E. Luzzi ◽  
L. D. Marks ◽  
M. I. Buckett
Keyword(s):  
Cross Correlation ◽  
A Priori ◽  
Matrix Material ◽  
Correlation Method ◽  
Accurate Knowledge ◽  
Complex Image ◽  
Fourier Filtering ◽  
The Matrix ◽  
Low Pass ◽  
Data Reduction Technique

As the HREM becomes increasingly used for the study of dynamic localized phenomena, the development of techniques to recover the desired information from a real image is important. Often, the important features are not strongly scattering in comparison to the matrix material in addition to being masked by statistical and amorphous noise. The desired information will usually involve the accurate knowledge of the position and intensity of the contrast. In order to decipher the desired information from a complex image, cross-correlation (xcf) techniques can be utilized. Unlike other image processing methods which rely on data massaging (e.g. high/low pass filtering or Fourier filtering), the cross-correlation method is a rigorous data reduction technique with no a priori assumptions.We have examined basic cross-correlation procedures using images of discrete gaussian peaks and have developed an iterative procedure to greatly enhance the capabilities of these techniques when the contrast from the peaks overlap.

Tandem scanning reflected light microscopy: How it works and applications

1986 ◽  
Vol 44 ◽  
pp. 84-87
Author(s):  
Alan Boyde ◽  
Milan Hadravský ◽  
Mojmír Petran ◽  
Timothy F. Watson ◽  
Sheila J. Jones ◽  
...  
Keyword(s):  
Light Microscopy ◽  
Focal Plane ◽  
Central Symmetry ◽  
Single Line ◽  
Scanning Microscope ◽  
Reflected Light ◽  
Illuminating Light ◽  
Illuminating Beam

The principles of tandem scanning reflected light microscopy and the design of recent instruments are fully described elsewhere and here only briefly. The illuminating light is intercepted by a rotating aperture disc which lies in the intermediate focal plane of a standard LM objective. This device provides an array of separate scanning beams which light up corresponding patches in the plane of focus more intensely than out of focus layers. Reflected light from these patches is imaged on to a matching array of apertures on the opposite side of the same aperture disc and which are scanning in the focal plane of the eyepiece. An arrangement of mirrors converts the central symmetry of the disc into congruency, so that the array of apertures which chop the illuminating beam is identical with the array on the observation side. Thus both illumination and “detection” are scanned in tandem, giving rise to the name Tandem Scanning Microscope (TSM). The apertures are arranged on Archimedean spirals: each opposed pair scans a single line in the image.

Towards 1-Ångstrom-resolution STEM

1993 ◽  
Vol 51 ◽  
pp. 996-997
Author(s):  
H.S. von Harrach ◽  
D.E. Jesson ◽  
S.J. Pennycook
Keyword(s):  
High Resolution ◽  
Field Emission ◽  
Phase Contrast ◽  
Spherical Aberration ◽  
A Priori ◽  
Dark Field ◽  
Image Resolution ◽  
Objective Lens ◽  
Annular Dark Field ◽  
First Results

Phase contrast TEM has been the leading technique for high resolution imaging of materials for many years, whilst STEM has been the principal method for high-resolution microanalysis. However, it was demonstrated many years ago that low angle dark-field STEM imaging is a priori capable of almost 50% higher point resolution than coherent bright-field imaging (i.e. phase contrast TEM or STEM). This advantage was not exploited until Pennycook developed the high-angle annular dark-field (ADF) technique which can provide an incoherent image showing both high image resolution and atomic number contrast.This paper describes the design and first results of a 300kV field-emission STEM (VG Microscopes HB603U) which has improved ADF STEM image resolution towards the 1 angstrom target. The instrument uses a cold field-emission gun, generating a 300 kV beam of up to 1 μA from an 11-stage accelerator. The beam is focussed on to the specimen by two condensers and a condenser-objective lens with a spherical aberration coefficient of 1.0 mm.

Treating Velopharyngeal Inadequacy Using Bilateral Buccal Flap Revision Palatoplasty

2019 ◽  
Vol 4 (5) ◽  
pp. 878-892
Author(s):  
Joseph A. Napoli ◽  
Linda D. Vallino
Keyword(s):  
Systematic Review ◽  
Obstructive Sleep Apnea ◽  
Sleep Apnea ◽  
Cleft Lip ◽  
Cleft Lip And Palate ◽  
A Priori ◽  
Sufficient Evidence ◽  
Obstructive Sleep ◽  
Before And After ◽  
Buccal Flap

Purpose The 2 most commonly used operations to treat velopharyngeal inadequacy (VPI) are superiorly based pharyngeal flap and sphincter pharyngoplasty, both of which may result in hyponasal speech and airway obstruction. The purpose of this article is to (a) describe the bilateral buccal flap revision palatoplasty (BBFRP) as an alternative technique to manage VPI while minimizing these risks and (b) conduct a systematic review of the evidence of BBFRP on speech and other clinical outcomes. A report comparing the speech of a child with hypernasality before and after BBFRP is presented. Method A review of databases was conducted for studies of buccal flaps to treat VPI. Using the principles of a systematic review, the articles were read, and data were abstracted for study characteristics that were developed a priori. With respect to the case report, speech and instrumental data from a child with repaired cleft lip and palate and hypernasal speech were collected and analyzed before and after surgery. Results Eight articles were included in the analysis. The results were positive, and the evidence is in favor of BBFRP in improving velopharyngeal function, while minimizing the risk of hyponasal speech and obstructive sleep apnea. Before surgery, the child's speech was characterized by moderate hypernasality, and after surgery, it was judged to be within normal limits. Conclusion Based on clinical experience and results from the systematic review, there is sufficient evidence that the buccal flap is effective in improving resonance and minimizing obstructive sleep apnea. We recommend BBFRP as another approach in selected patients to manage VPI. Supplemental Material https://doi.org/10.23641/asha.9919352

Project MATCH secondary a priori hypotheses

Addiction ◽  
1997 ◽  
Vol 92 (12) ◽  
pp. 1671-1698 ◽  
Author(s):  
Project Match Research Group
Keyword(s):  
A Priori ◽  
Project Match

Vergleich einer Papier-Bleistift- und einer computergestützten Version des Leistungsprüfsystems (LPS)

Diagnostica ◽  
2002 ◽  
Vol 48 (3) ◽  
pp. 115-120 ◽  
Author(s):  
Stefan Troche ◽  
Beatrice Rammstedt ◽  
Thomas Rammsayer
Keyword(s):  
A Priori

Zusammenfassung. Der zunehmende Einsatz computergestützter diagnostischer Verfahren führt zwangsläufig zur Frage nach der Äquivalenz zwischen konventionellen Papier-Bleistift-Versionen und entsprechenden Computertranspositionen. Zur Überprüfung der Äquivalenz zwischen der computergestützten Version des Leistungsprüfsystems (LPS) im Hogrefe Testsystem und der Papier-Bleistift-Version wurden 131 Versuchspersonen mit beiden Verfahren getestet. Heterogene Ergebnisse zwischen der Papier-Bleistift- und der Computerversion belegen, dass nicht a priori von der Äquivalenz beider Versionen ausgegangen werden kann, und weisen nachdrücklich auf die Notwendigkeit systematischer Äquivalenzprüfungen hin. Eine an Hand einer zweiten Stichprobe von 40 Testpersonen durchgeführte Überprüfung der Retest-Reliabilität der computergestützten Version des LPS ergab für ein Retest-Intervall von zwei Wochen Reliabilitätskoeffizienten zwischen rtt = 0.55 und rtt = 0.94. In der Diskussion werden mögliche Gründe für die Nicht-Äquivalenz der beiden LPS-Versionen identifiziert.

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